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Building Efficient Light-Matter Interfaces for
MA SSACHUSETTS INSTITUTE
Quantum Systems
OF TECHNOLOGY
by
NOV 0 2 2015
Tsung-Ju Jeff Lu
LIBRARIES
B.S. Electrical Engineering, California Institute of Technology (2013)
Submitted to the Department of Electrical Engineering and Computer
Science
in partial fulfillment of the requirements for the degree of
Master of Science in Electrical Engineering and Computer Science
at the
MASSACHUSETTS INSTITUTE OF TECHNOLOGY
September 2015
@ Massachusetts Institute of Technology 2015. All rights reserved.
Author ....
Signature redacted
Depart(ent oiElectrifal Engine1ering and Computer Science
August 28, 2015
Cetfidby..Signature
by. .
Certified
redacted
............
Dirk R. Englund
Assista t Pro ssor of Electrical Engineering
Thesis Supervisor
Accepted by....Signature
redacted
/
0 Wofessor Leslie A. Kolodziejski
Chair of the Committee on Graduate Students
2
Building Efficient Light-Matter Interfaces for Quantum
Systems
by
Tsung-Ju Jeff Lu
Submitted to the Department of Electrical Engineering and Computer Science
on August 28, 2015, in partial fulfillment of the
requirements for the degree of
Master of Science in Electrical Engineering and Computer Science
Abstract
Efficient collection of photons from quantum memories, such as quantum dots (QDs)
and nitrogen vacancy (NVs) centers in diamond, is essential for various quantum
technologies. This thesis describes the design, fabrication, and utilization of novel
photonic structures and systems to achieve potentially world-record photon collection
from quantum dots. This technique can also be applied to NVs in diamond in the
near future.
Also, the NV- charged state has second-scale coherence times at room temperature that make it a promising candidate for solid state memories in quantum computers and quantum repeaters. NV- is an individually addressable qubit system
that can be optically initialized, manipulated, and measured. On-chip entanglement
generation would be the basis of scalability for quantum information processing technologies. These properties have enabled recent demonstrations of heralded quantum
entanglement and teleportation between two separated NV centers. To improve the
entanglement probability in such schemes, it is imperative to improve the efficiency
with which single photons from a NV center can be guided into a low-loss single-mode
waveguide. As such, a second component of this thesis focuses on the development
of a photonic integrated circuit based on aluminum nitride that would incorporate
pre-selected, long-lived NV center quantum memories as well as pre-selected, highperformance superconducting nanowire single-photon detectors (SNSPDs). This hybrid device would have the capability to perform on-chip entanglement of photons
from separate quantum memories to build up a quantum repeater necessary for longdistance quantum communication and distributed quantum computing.
Thesis Supervisor: Dirk R. Englund
Title: Assistant Professor of Electrical Engineering
3
4
Acknowledgments
This thesis would not have been possible without the guidance of many people. First
of all, I would like to acknowledge my advisor, Professor Dirk Englund, for his guidance and support.
It has been a real privilege to work with Professor Englund,
learning directly from him, and always being able to ask him for advice on anything.
He has played such a large role in shaping my academic and research interests and
helping me reach my goals that I would like to thank him for that.
I would also like to thank everyone in the Quantum Photonics Laboratory for their
help in everything. I have truly learned so much in the past two years from everyone
in the group. I feel like I am a better researcher and person as a result. It is amazing
to work with this group of highly intelligent and extremely motivated academics. It
is really a blessing to be in such a wonderful work environment. I particularly want
to thank Dr. Gabriele Grosso for helping me with the fiber-integrated single photon
source project in this thesis. He worked with me on building the optical setup and
mentored me in doing the spectroscopy experiments.
Also, I would like to thank my collaborators Ryan Camacho, Matt Eichenfield, Ian
Frank, and Jeremy Moore from Sandia National Laboratories. Although I only visited
for one week, it was a great experience to see what it was like to work in a national
lab. I appreciated all of you making me feel welcomed. I enjoyed Albuquerque very
much and look forward to visiting more in the future for our collaboration.
In addition, I would like to thank Jim Daley and Mark Mondol of NanoStructures
Laboratory for all their help and expertise in fabrication. Furthermore, I would like to
thank Eric Lim, Dave Terry, Bob Bicchieri, and the rest of Microsystems Technology
Laboratories for all their help and expertise in fabrication as well.
Developing a
reliable fabrication process was a difficult part in this Master's Thesis, so I am grateful
to all these people for helping me with this huge obstacle.
Finally, I want to give my utmost thanks to my mother and father for their love,
care, and countless sacrifice they have made for my education. They have been my
guiding light in every difficult and important decision throughout my life. They are
5
very supportive in everything I do, and I live to make them proud. Thank you so
much for being the best parents imaginable.
6
Contents
Introduction
17
Progress and Challenges of Using Epitaxial Quantum Dots .
20
Nitrogen Vacancy Center in Diamond . . . . . . . . . . . . . . . . .
20
1.2.1
. . . . . . . . . . . . . . . . . . . . . . .
20
Thesis O utline . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
22
1.3
.
Fiber-Integrated Single Photon Source
23
Motivation and Goals . . . . . . . . .
. . . . . . . . .
23
2.2
Bullseye Grating Structure . . . . . .
. . . . . . . . .
24
2.2.1
Previous Studies
. . . . . . .
. . . . . . . . .
24
2.2.2
Pick-and-Place Method . . . .
. . . . . . . . .
24
2.2.3
Modifications in Structure . .
. . . . . . . . .
25
.
.
.
.
.
2.1
Fabrication
. . . . . . . . . . . . . .
. . . . . . . . .
28
2.4
Experimental Results . . . . . . . . .
. . . . . . . . .
30
2.4.1
Optical Setup . . . . . . . . .
. . . . . . . . .
30
2.4.2
Spectroscopy Experiments . .
. . . . . . . . .
33
.
.
2.3
.
2
NV- defect center
.
1.2
.
1.1.1
.
. . . . . . . . . . . . .
Self-assembled semiconductor quantum dots
.
1.1
17
.
1
3 Quantum Repeater using NV and Wide-Bandgap Programmable
Nanophotonic Processor
37
Overview and Vision ........
. . . . . . . . . . . . . . . . . . .
37
3.2
Aluminum Nitride . . . . . . . . .
. . . . . . . . . . . . . . . . . . .
39
.
3.1
3.2.1
Sandia National Laboratories' AlN Fabrication Process
7
39
4
Mask Patterns for Sandia Process . . . . . . . . . .
41
.
3.3
Passive Components of Aluminum Nitride Photonic Integrated Circuit
Adiabatic Waveguide Taper
. . . . . . . . . . . . .
49
4.2
Bragg Grating Filter . . . . . . . . . . . . . . . . .
50
4.3
Disk Resonator
. . . . . . . . . . . . . . . . . . . .
54
4.3.1
Dependence on Coupling Gap . . . . . . . .
54
4.3.2
Dependence on Coupling Length
. . . . . .
57
4.3.3
Plans for Better Design . . . . . . . . . . . .
60
.
.
.
.
.
61
4.4.1
Analytical Calculations . . . . . . . . . . . .
61
4.4.2
Variational FDTD Simulations . . . . . . . .
63
4.4.3
3D FDTD Simulations . . . . . . . . . . . .
65
.
. . . . . . . . .
.
.
.
Directional Coupler for 50:50 Split
69
In- House Fabrication and Fast Prototyping
70
Grating Couplers . . . . . . . . . . . . . . . . .
71
.
First Generation Test Structures . . . . . . . . . . . . .
5.1.1
.
5.1
6
.
4.1
4.4
Fabrication
. . . . . . . . . . . . . . . . . . . . . . . .
72
5.3
Experimental Results . . . . . . . . . . . . . . . . . . .
76
5.3.1
Confocal Setup
. . . . . . . . . . . . . . . . . .
76
5.3.2
Confocal Microscopy Experiments . . . . . . . .
78
.
.
.
5.2
.
5
49
Conclusions and Future Work
81
8
List of Figures
1-1
Simplified depiction of the excited electron and the hole in an exciton entity
and the corresponding energy levels. The total energy is the sum of the band
gap energy between the occupied level and unoccupied energy level, the energy involved in the Coulomb attraction in the exciton, and the confinement
energies of the excited electron and the hole [24].
. . . . . . . . . . . . .
18
. . . . .
21
1-2
Schematic of the nitrogen vacancy center in the diamond lattice.
2-1
(a) Pick-and-place membrane transfer of an SNSPD onto a waveguide. (b)
Suspended SNSPD membrane.
(c) SNSPD membrane that was removed
from the carrier chip using a tungsten microprobe with a drop of hardened
PDMS at the tip. (d) SNSPD membrane integrated to a silicon waveguide
[151 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2-2
24
(a) Modification of bullseye structure for completely suspended structures.
(b) Design for creating bullseye membranes that can be picked out. ....
9
25
2-3
This is a comparison using the FDTD software Lumerical to see the difference
between the original partial etch bullseye structure in Davanco et al. and the
full etch modified bullseye structure we developed. For these simulations, the
quantum dot dipole was assumed to be oriented along the xy plane, which
means only the TE slab waves were excited. (a) and (b) show the simulation
layout of partial etch bullseye structure, with a quantum dot dipole placed
at the center of the structure. (c) Purcell enhancement spectrum associated
with (a) and (b), which shows that the resonant wavelength is 951 nm and
Q
is 308. (d) and (e) show the simulation layout of the modified bullseye
structure with suspension bridges to hold the structure when the trenches
are fully etched, with a quantum dot dipole placed at the center of the
structure. (f) Purcell enhancement spectrum associated with (d) and (e),
which shows that the resonant wavelength is 940 nm and
2-4
Q is
485. ....
26
(a) and (b) show the simulation layout of the complete bullseye membrane
on top of a fiber facet system. (b) Electric field intensity in the xy plane. (c)
Far-field polar plot of the cavity mode. (d) Purcell enhancement spectrum,
which shows that the resonant wavelength of the entire system is 945 nm
and
2-5
Q
is 358. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
27
This is a comparison using the FDTD software Lumerical to see the difference
between the original partial etch bullseye structure in Davanco et al. (left
half) and the full etch modified bullseye structure we developed (right half).
The top images are the log scale Electric field intensity of the circular grating
structure in the xz plane. The bottom images show the percentage of total
emission collected by NA = 0.5 optics as a function of wavelength. ....
2-6
Starting substrate of the quantum dot wafers. The InAs quantum dots are
embedded near the center of the GaAs layer. . . . . . . . . . . . . . . . .
2-7
28
28
(a) Left: design, right: fabricated structures of "bullseye" circular grating (b)
Left: design, right: fabricated structures of "bullseye" circular grating with
suspended bridges that can be broken to systematically place the structure
on a fiber facet.
. . . . . . . . ..
10
. . . . . . . . . . . . . . . . . . . .
30
2-8
4F imaging configuration [101.
2-9
Experimental setup for quantum dot experiments.
. . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . .
2-10 (a) Microscope objective directly over Montana cryostat.
31
32
(b) Portion of
setup that transitions from the elevated optical platform to the optical table.
32
2-11 (a) Confocal scan of the fluorescence of an array of bullseye circular gratings.
(b) Zoomed-in confocal scan of the fluorescence of one bullseye circular grating. Note: the dimensions on the side are not the actual physical dimensions
of the scan, but rather the voltage applied to each galvos mirror.
2-12 Spectrum of the bulk quantum dots at an unpatterned area.
. . . . .
33
. . . . . . .
34
2-13 Spectrum at the center of a bullseye structure with a bright enhanced fluorescence spot.
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
34
2-14 Spectrum at the center of a bullseye structure with a bright enhanced fluorescence spot, using a higher density grating and lower pump power.
3-1
. . .
35
Overview of quantum repeater hardware, which uses nitrogen vacancy centers in diamond as quantum registers, AlN photonic integrated circuit for
dynamic photonic routing, and SNSPDs as on-chip detectors. . . . . . . .
3-2
Complete device overview of Sandia National Laboratories' AlN optomechanically tunable microdisk that can serve as an optical filter.
3-3
. . . . . . . . . . . . . . . . . . . . . . . . . . . . .
40
40
Condensed overview of the mask patterns for each MZI element. All masks
for the 6 layers are overlapped and displayed.
3-5
. . . . . .
Fabrication process of Sandia National Laboratories' AlN optomechanically
tunable microdisk.
3-4
38
. . . . . . . . . . . . . . .
41
Top-down view depicting a NV nanobeam cavity membrane integrated to
the AlN photonic waveguide network. This also shows the proximity of the
microwave striplines with respect to the NV nanobeam cavity.
3-6
. . . . . .
43
Side view depicting a NV nanobeam cavity membrane integrated to the AlN
photonic waveguide network. This also shows the proximity of the microwave
striplines with respect to the NV nanobeam cavity.
11
. . . . . . . . . . . .
44
3-7
Top-down view depicting a SNSPD membrane integrated to the AIN photonic waveguide network. The SNSPD gold pads make contact with the
gold pads on the chip so that the larger contact pads can be wirebonded to
electrically operate the SNSPD.
3-8
. . . . . . . . . . . . . . . . . . . . . .
44
Side view depicting a SNSPD membrane integrated to the AlN photonic
waveguide network. The SNSPD gold pads make contact with the gold pads
on the chip so that the larger contact pads can be wirebonded to electrically
operate the SNSPD.
3-9
. . . . . . . . . . . . . . . . . . . . . . . . . . . .
Mask patterns for making the tunable microdisk.
45
(a) Pattern 1 for the
nitride etch in step 2. (b) Pattern 2 for the bottom electrode etch in step
4. (c) Pattern 3 for etching through the AIN and bottom electrode to the
tungsten layer in step 9. (d) Pattern 4 for the AlCu etch in step 10. (e)
Pattern 5 for etching through the AlN and oxide to the nitride layer in step
12. (f) Overview of the mask patterns for each tunable microdisk. All masks
for the 6 layers are overlapped and displayed.
. . . . . . . . . . . . . . .
46
3-10 Mask patterns for making the rest of the MZI. (a) The rest of pattern 5 for
defining the AIN structures. (b) Pattern 6 for the metal liftoff step after
step 12. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4-1
47
Adiabatic waveguide taper for coupling light efficiently from diamond nanobeam
cavities to AlN waveguide. This design is taken exactly as-is from Mouradian
et al.'s 2014 paper [141. . . . . . . . . . . . . . . . . . . . . . . . . . . .
4-2
50
(a) Overall design of Bragg Grating filter, which is used for filtering the 532
nm green excitation laser and allowing the 637 nm NV fluorescence to pass
through.
(b) Dimensions of the Bragg Grating filter, where the period is
144 nm, the original waveguide width is 400 nm, the corrugated waveguide
width is 280 nm, and the thickness of the waveguide is 200 nm. (c) Electric
field profile of the larger width 400 nm cross section, which has an effective
mode index of 1.89868. (d) Electric field profile of the smaller width 280 nm
corrugated cross section, which has an effective mode index of 1.810855.
12
.
.
50
4-3
(a) Bandstructure spectrum at the band edge k- = ir/a. (b) Transmission
spectrum for 5000 periods. (c) Transmission spectrum for 8000 periods.
4-4
.
53
(a) Simulation setup for a disk resonator of 30 pLm coupled to two bus waveguides by a coupling length of 12.3890 Rm and coupling gap of 200 nm. The
input port is at the top left, the through port is at the top right, and the
drop port is at the bottom left. (b) Transmission spectrum of the through
port. (c) Transmission spectrum of the drop port.
4-5
. . . . . . . . . . . .
55
(a) Simulation setup for a disk resonator of 30 pm coupled to two bus waveguides by a coupling length of 12.3890 pm and coupling gap of 100 nm. The
input port is at the top left, the through port is at the top right, and the
drop port is at the bottom left. (b) Transmission spectrum of the through
port. (c) Transmission spectrum of the drop port.
4-6
. . . . . . . . . . . .
56
(a) Simulation setup for a disk resonator of 30 prm coupled to two bus waveguides by a coupling length of 12.3890 pm and coupling gap of 50 nm. The
input port is at the top left, the through port is at the top right, and the
drop port is at the bottom left. (b) Transmission spectrum of the through
port. (c) Transmission spectrum of the drop port ..
4-7
. . . . . . . . . . . .
57
(a) Simulation setup for a disk resonator of 30 pm coupled to two bus waveguides by a coupling length of 60 pLm and coupling gap of 50 nm. The input
port is at the top left, the through port is at the top right, and the drop
port is at the bottom left. (b) Transmission spectrum of the through port.
(c) Transmission spectrum of the drop port.
4-8
. . . . . . . . . . . . . . .
58
(a) Simulation setup for a disk resonator of 30 pLm coupled to one bus waveguide by a coupling length of 100 pim and coupling gap of 200 nm. The input
port is at the bottom left and the through port is at the bottom right.
(b) Spectrum of the
Q
factor of the disk as a function of wavelength. (c)
Transmission spectrum of the through port. . . . . . . . . . . . . . . . .
13
59
4-9
(a) Simulation setup for a disk resonator of 30 Rm coupled to one bus waveguide by a coupling length of 150 ptm and coupling gap of 200 nm. The input
port is at the bottom left and the through port is at the bottom right.
(b) Spectrum of the
Q
factor of the disk as a function of wavelength. (c)
Transmission spectrum of the through port. . . . . . . . . . . . . . . . .
60
4-10 (a) Simulation setup for solving the eigenmode of two straight waveguides
coupled evanescently to each other.
of the symmetric supermode.
antisymmetric supermode.
(b) Real part of the Ey modal field
(c) Real part of the Ey modal field of the
. . . . . . . . . . . . . . . . . . . . . . . . .
62
4-11 (a) 2.5D variational FDTD simulation setup for solving the splitting ratio
of a directional coupler with bend radius of 20 pm and coupling length of
60.673 pLm. Bottom left hand is the location of the input mode of waveguide
1, bottom right hand is the location of the output mode of waveguide 1, and
the top right hand is the location of the output mode of waveguide 2. (b)
Electric field profile of the entire propagation structure. (c) Transmission of
power through the waveguide 1 input. (d) Transmission of power through
the waveguide 1 output. (e) Transmission of power through the waveguide
2 output.
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
64
4-12 (a) 3D FDTD simulation setup for solving the splitting ratio of a directional
coupler with bend radius of 20 pim and coupling length of 60.673 pm. Bottom
left hand is the location of the input mode of waveguide 1, bottom right hand
is the location of the output mode of waveguide 1, and the top right hand
is the location of the output mode of waveguide 2. (b) Electric field profile
of the entire propagation structure. (c) Transmission of power through the
waveguide 1 input.
(d) Transmission of power through the waveguide 1
output. (e) Transmission of power through the waveguide 2 output.
Electric field mode profile of the waveguide 1 input.
14
(f)
. . . . . . . . . . .
65
4-13 (a) 3D FDTD simulation setup for solving the splitting ratio of a directional
coupler with bend radius of 20 pm and coupling length of 23.43 pLm. Bottom
left hand is the location of the input mode of waveguide 1, bottom right hand
is the location of the output mode of waveguide 1, and the top right hand
is the location of the output mode of waveguide 2. (b) Electric field profile
of the entire propagation structure. (c) Transmission of power through the
waveguide 1 input.
output.
(d) Transmission of power through the waveguide 1
(e) Transmission of power through the waveguide 2 output.
Electric field mode profile of the waveguide 1 input.
(f)
. . . . . . . . . . .
66
5-1
Starting substrate of the aluminum nitride on sapphire wafers.
5-2
Structure for testing waveguide loss.
5-3
Structure for testing directional coupler splitting.
5-4
Side view of chip after HSQ patterning and Cr dry etch.
5-5
50x microscope image of structure for testing directional coupler splitting.
75
5-6
50x microscope image of structure for testing waveguide loss.
. . . . . . .
75
5-7
100x microscope image of structure for testing waveguide loss.
. . . . . .
76
5-8
Atomic force microscopy scan of a portion of the AlN waveguide.
. . . . .
76
5-9
Atomic force microscopy scan of an AlN grating coupler.
. . . . . . . . .
76
. . . . . .
69
. . . . . . . . . . . . . . . . . . .
70
. . . . . . . . . . . . .
70
. . . . . . . . .
74
5-10 Picture of the sample stage portion of the experimental setup, where the left
stage is the sample stage and the right Thorlabs stage is the piezo stage for
positioning the fiber.
. . . . . . . . . . . . . . . . . . . . . . . . . . .
77
5-11 Region of the output grating coupler in the confocal scan window. Image is
taken by exciting and collecting the reflection using the confocal microscope.
78
5-12 Confocal scan when pumping with the fiber at the input grating and collecting the light from the output grating by using the confocal microscope.
15
79
16
Chapter 1
Introduction
1.1
Self-assembled semiconductor quantum dots
On-demand single photon sources are necessary for many quantum technologies, particularly quantum key distribution, where it is imperative to have single photons
with known polarizations. On-demand single photon sources also have applications
in quantum computation using only linear optics, as well as quantum repeaters for
quantum optical communication. Typically, on-demand single photon sources involve
a dipole transition in a two-level quantum system. Self-assembled epitaxially-grown
semiconductor quantum dots (QDs) are one of the best candidates for on-demand single photon sources today since about 90% of the photons emitted from it are emitted
in the zero-phonon line. Also, they have good multi-photon suppression, as well as
quantum-mechanically indistinguishability between consecutive photons. In the case
of self-assembled semiconductor quantum dots, a charged carrier decays from a highenergy state to a low-energy state and releases a single photon in the process with
wavelength -,
where AE is the energy difference between the two energy levels.
A quantum dot is a nanometer-sized semiconductor nanocrystal that confines
charge carriers (excitons) in all directions and in a small volume (around the same
order in size as the exciton Bohr radius or smaller); it needs to be small enough so
that the excitons can interact. They behave as artificial atoms that exhibit quantum
mechanical properties and have well-defined energy levels. The quantum confinement
17
of electron-hole pairs (excitons) and electrostatic interaction between electrons and
holes inside the quantum dot result in a discrete spectrum. It is easy to tune the
emission wavelength of a quantum dot during fabrication. The larger the quantum
dot, the larger the emission wavelength.
However, one cannot simply increase the
size of a quantum dot indefinitely either since it needs to be small enough to be in
the strong confinement regime so that the optical properties are tunable. The exciton
Bohr radius is given by:
a* = Er(m) ab
b
where
ab
(1.1)
A
is the Bohr radius (which is material dependent), m is the mass, p is the
reduced mass, and E, is the size-dependent dielectric constant.
Exciton
(electron-hole pair)
FD
( ) Band gap
Zero point vibrational
D energy of the excited
electron
I
0 0
Zeo point vibrational
11 energy of the hole
Figure 1-1: Simplified depiction of the excited electron and the hole in an exciton entity
and the corresponding energy levels. The total energy is the sum of the band gap energy
between the occupied level and unoccupied energy level, the energy involved in the Coulomb
attraction in the exciton, and the confinement energies of the excited electron and the hole
[24].
As shown in Figure 1-1, to make the quantum dot fluoresce, an electron is first
excited to the conduction band, usually by photo-pumping with a laser with lower
wavelength than the band gap. This leaves behind a hole in the valence band. Then
18
fluorescence is achieved when the excited electron relaxes to the ground state and
combines with a hole. The emitted photon energy E is the sum of:
1. The band gap energy
Ebandgap
between the occupied level and the unoccupied
energy level.
2. Confinement energies of the hole and the excited electron. Since the exciton in
a quantum dot can be treated as a particle in a box, the confinement energy of
the exciton can be varied by changing the quantum dot size:
Econf inement
h2 2
2a2
1
(Me
+
h272
-
2
Mh
where a is the radius, me is the electron mass,
2pa
mh
(1.2)
is the hole mass, and p is the
reduced mass.
3. Bound energy of the exciton, which is a bound state of an electron and a hole
held together by attractive electrostatic Coulomb forces:
Eexciton =
=
-
R*
(1.3)
where E, is the size-dependent dielectric constant, p is the reduced mass, me is
the free electron mass, and RY
=
13.6eV is the Rydberg constant.
In summary, the emitted photon energy E is given by the following equation, which
shows that the luminescence is typically red-shifted with respect to the excitation
light and varying the size of the quantum dot can tune the emission energy:
E
=
Ebandgap + Econfinement + Eexciton
=
Ebandgap +
22
- R*
(1.4)
For this thesis, I will be using Indium Arsenide (InAs) quantum dots epitaxially grown on Gallium Arsenide (GaAs). Specifically, the quantum dots are created
using self-assembled growth by Stransky-Krastanov molecular beam epitaxy.
19
The
self-assembly growth leads to variations in size of the quantum dots and variations
in the InGaAs composition, which causes an inhomogeneous distribution of emission
wavelength. Physically, the quantum dots are disk-like shaped with dimensions of
about 5nm tall and 20 to 40nm in diameter. Since the transitions are influenced by
the QD size, QD height, and InGaAs composition, these quantum dots usually emit
single photons with wavelength around 940nm, with a FWHM of around 20-30nm.
1.1.1
Progress and Challenges of Using Epitaxial Quantum
Dots
Even with all the advancements in harnessing epitaxial quantum dots as on-demand
single photon sources, the efficient extraction of light is still a big challenge today and
is essential for many applications in quantum information processing. The emitted
single photons from QDs suffer from total internal reflection at the semiconductorair interface since epitaxial quantum dots are embedded in semiconductor material.
Previous attempts at surmounting this problem include micropillar [211 cavities and
photonic crystal cavities
181. However, this requires spectral tuning of the cavity
resonance to the QD emission line. Bulk epitaxial quantum dots have a broadband
spectrum, so spectral tuning of the cavity resonance to a QD that is spatially aligned
to a cavity center is very difficult. Being able to develop a system that is operational
for broadband wavelengths while offering Purcell enhancement for improving photon
collection would help create the ideal on-demand single photon source.
1.2
1.2.1
Nitrogen Vacancy Center in Diamond
NV- defect center
The nitrogen vacancy (NV) color defect center in diamond has been the subject of
intense research efforts in recent years because it is fluorescent and has unique spin
properties.
Specifically, the singly negatively charged NV- center is a promising
candidate for solid state spin qubit in quantum information processing [7, 161. The
20
Figure 1-2: Schematic of the nitrogen vacancy center in the diamond lattice.
NV defect center consists of a substitutional nitrogen atom and neighboring vacancy
191. It has two fluorescent charge states NV
-
in the diamond lattice (Figure 1-2)
and NV'. The NV- has a ground state spin triplet that is promising for numerous
applications while the NV 0 is less studied and is generally considered undesirable. The
two charge states have distinct electronic structure and therefore different fl uorescence
intensities as well as spectra.
Researchers around the world have demonstrated various quantum technologies,
including quantum entanglement 1231, teleportation [181, and sensing 1221, by taking
advantage of the unequaled optical and spin properties of NVs in diamond. In order to
achieve faster quantum information processing
131 and better sensitivity in metrology,
it is necessary to have efficient routing and detection of the NV photoluminescence.
Typically, the total internal reflection confinement due to the high refractive index
of diamond limits efficient photon collection.
Previous attempts at this challenge
in bulk diamond use techniques such as vertical pillars
121, solid immersion lenses.,
photonic crystal cavities [191, etc. to achieve photon collection rates of about one
million counts per second. Being able to push this number far beyond that offered by
current technology is important for performing single shot readout of NVs at room
temperature.
21
1.3
Thesis Outline
Efficient collection of photons from quantum memories, such as quantum dots and nitrogen vacancy centers in diamond, is essential for various quantum technologies. This
thesis shows efforts toward this by integrating a "bullseye" circular grating structure
for quantum dots onto a fiber facet, which can also be extended to NVs in diamond
[12, 11. Doing so would take advantage of the lower index contrast of the diamond(semiconductor-) glass interface compared to the diamond- (semiconductor-) air interface to have preferentially most of the dipole emission emitting into the fiber.
Integrating these quantum emitters directly onto optical fibers would eliminate collection loss in unnecessary free-space optical components [171. Also, it would achieve
a compact system that can be a plug-and-play for quantum information processing
applications.
In addition, the NV- nuclear spin state has second-scale coherence times at room
temperature that makes it a promising candidate for solid state memories in quantum
computers and quantum repeaters [131.
NV- is an individually addressable qubit
system that can be optically initialized, manipulated, and measured [6].
On-chip
entanglement generation would be the basis of scalability for quantum information
processing technologies. These properties have enabled recent demonstrations of heralded quantum entanglement and teleportation between two separated NV centers
[3J.
To improve the entanglement probability in such schemes, it is imperative to improve
the efficiency with which single photons from an NV center can be guided into a lowloss single-mode waveguide. As such, a second portion of my master's thesis would be
to develop and build up a photonic integrated circuit based on aluminum nitride
1261
that would incorporate pre-selected, long-lived NV center quantum memories [141 as
well as pre-selected, high-performance superconducting nanowire single-photon detectors (SNSPDs) [151. This hybrid device would have the capability to perform on-chip
entanglement of photons from separate quantum memories to build up a quantum
repeater necessary for long-distance quantum communication.
22
Chapter 2
Fiber-Integrated Single Photon
Source
2.1
Motivation and Goals
The motivation for this portion of my thesis is that the single-photon rate of epitaxial
QDs is limited by collection efficiency, rather than generation rate. The high refractive index contrast between GaAs (n = 3.4) and air causes the collection efficiency
to be < 1%. Photonic crystals have been shown to offer radiative rate enhancement
for efficient outcoupling, as well as improved single photon rate and photon indistinguishability. However, the drawback of using photonic crystals is that high
Q
factor
means narrow spectral band, which makes it difficult to both spectrally and spatially
line up a quantum dot to a photonic crystal cavity.
We propose to utilize a bulls-
eye microcavity for broadband efficient photon extraction. As such, the goal for this
portion is to demonstrate efforts toward fiber-integration of bullseye structures using
pick-and-place. This would obviate an optical setup for photon extraction from QDs.
We envision this system to be a potential plug-and-play device that can be placed in
a cryostat, with the excitation and collection using the same access fiber.
23
2.2
2.2.1
Bullseye Grating Structure
Previous Studies
The bullseye microcavity structure was first introduced by Davanco et al. in 2011 [5].
It is based on high-contrast second-order Bragg gratings, where the period is equal
to the guided wave wavelength:
A = AQD/nTE
where
AQD
(2.1)
is the emission wavelength of the quantum dot and nTE is the GaAs slab
TE mode effective index.
This structure favors vertical light extraction that would have otherwise radiated
into slab-guided modes. These periodic bullseye structures create a cavity resonance,
which is caused by partial reflections at the gratings toward the center. Furthermore,
the large index contrast at trenches results in strong reflections and out-of-plane
scattering. Davanco et al. showed by using a far-field polar plot for the cavity mode
that the collection efficiency is 53% for NA = 0.42 objective. In addition, the emitted
field is nearly Gaussian and contained within 20' half-angle.
2.2.2
Pick-and-Place Method
Au
- -
A()
Aur
Figure 2-1: (a) Pick-and-place membrane transfer of an SNSPD onto a waveguide. (b)
Suspended SNSPD membrane. (c) SNSPD membrane that was removed from the carrier
chip using a tungsten microprobe with a drop of hardened PDMS at the tip. (d) SNSPD
membrane integrated to a silicon waveguide [151.
24
We will integrate the bullseye membranes to a fiber by utilizing the pick-andplace membrane transfer method previously shown in our group by Najafi et al. [151.
Figure 2-1 is obtained from [151 to show how the pick-and-place method works. The
important take-away is shown in Figure 2-1(b), which shows the design that results
in sturdy bridges for holding the membrane in place after undercut but still brittle
enough to easily break off with a tungsten microprobe during membrane transfer.
2.2.3
Modifications in Structure
(a)
(b)
Figure 2-2: (a) Modification of bullseye structure for completely suspended structures. (b)
Design for creating bullseye membranes that can be picked out.
As shown Figure 2-2(a), we have the modified design for the bullseye structure to
be used for our purposes. Due to the nature of pick-and-place, the bottom surface of
the membrane will be placed on top of the fiber facet. As such, we want fully etched
trenches since it is currently not possible to correctly orient structures with partially
etched trenches. As a result, this modified bullseye structure would have the same
upward and downward emissions. In Figure 2-2(b), we have suspension bridges and
large areas for undercut and prying that can be used to pick out the fully-suspended
bullseye membranes. This provides an unpatterned surface area for the pick-and-place
tungsten probe to adhere to without breaking the bullseye structure.
In order to show the result of modifying and optimizing the original bullseye structure, a commercial Finite-Difference Time-Domain (FDTD) solver software called
Lumerical was used to compare the cavity mode and Purcell enhancement factor of
each. From the results shown in Figure 2-3, we can see the behavior of the origi-
25
=951 nm
Q =308
X =940 nm
Q = 485
Figure 2-3: This is a comparison using the FDTD software Lumerical to see the difference
between the original partial etch bullseye structure in Davanco et al. and the full etch
modified bullseye structure we developed. For these simulations, the quantum dot dipole
was assumed to be oriented along the xy plane, which means only the TE slab waves were
excited. (a) and (b) show the simulation layout of partial etch bullseye structure, with a
quantum dot dipole placed at the center of the structure. (c) Purcell enhancement spectrum
associated with (a) and (b), which shows that the resonant wavelength is 951 nm and Q
is 308. (d) and (e) show the simulation layout of the modified bullseye structure with
suspension bridges to hold the structure when the trenches are fully etched, with a quantum
dot dipole placed at the center of the structure. (f) Purcell enhancement spectrum associated
with (d) and (e), which shows that the resonant wavelength is 940 nm and Q is 485.
nal bullseye cavity (top half) with that of the modified fully-etched bullseye cavity
(bottom half). As shown, the fully etched trenches result in better field confinement,
which results in higher cavity
Q and
higher Purcell factor. This means that this would
potentially give a g(2 ) (0) that would be higher than zero due to the multiexcitonic and
hybridized. QD-wetting layer states being coupled to the cavity. Also, the full-etch
design results in a blue-shift in the cavity mode.
Figure 2-4 shows the Lumerical simulation results of the complete system where
the bullseye membrane is placed at the end of a fiber. The changes we had to make in
the simulation compared to the design in Davanco et al. was that we have a different
GaAs layer thickness (160 nm for our's vs. 190 nm for their's). As such, there is a
difference in the TE mode effective index, which results in significant blue-shift. As
a result, in order to maintain around the same resonant wavelength for the structure,
we increased the grating period to compensate. Bridges were also incorporated in the
bullseye structure in order to hold together the entire structure when the membrane
26
(a)
A
I4,0
(b)
32
7
C
-1
0
t
x(microns)
(C)
120
30
24
,
-1 8
300
240
25
(d)
06
-
330
210
Re(purcel)
2015-
A=945 nm
Q = 358
10
Ud
IIl 1,1
U3do0 U.951 1IUO
Iar~da(rnicrons)
Figure 2-4: (a) and (b) show the simulation layout of the complete bullseye membrane on
top of a fiber facet system. (b) Electric field intensity in the xy plane. (c) Far-field polar
plot of the cavity mode. (d) Purcell enhancement spectrum, which shows that the resonant
wavelength of the entire system is 945 nm and Q is 358.
is completely suspended.
fiber.
Also, a glass slab was included to represent the optical
The structure was tuned and modified so that the xy electric field intensity
and far-field polar plot remain the same, that way the emitted field remains nearly
Gaussian and contained within 20' half-angle.
Figure 2-5 shows a comparison of our system with the original bullseye structure.
0ur's
Davanco, M. et al.
10
0
100
2n
o
3001M2I
50800
O3W00
Percentage of total
emission collected by
NA =0.5 optics
"j
Figure 2-5: This is a comparison using the FDTD software Lumerical to see the difference
between the original partial etch bullseye structure in Davanco et al. (left half) and the
full etch modified bullseye structure we developed (right half). The top images are the log
scale Electric field intensity of the circular grating structure in the xz plane. The bottom
images show the percentage of total emission collected by NA = 0.5 optics as a function of
wavelength.
We see that the percentage of total emission collected by NA = 0.5 optics for our
system is about half compared to the original structure. However, we expect a higher
experimental collection efficiency in practice due to direct coupling into fiber. That
is because the paper involves free space optics, which typically has some loss.
2.3
Fabrication
GaAs (160 [nm])
Alo.9Gao.iAs
(800 [nml-1 [pm])
GaAs
Figure 2-6: Starting substrate of the quantum dot wafers. The InAs quantum dots are
embedded near the center of the GaAs layer.
Figure 2-6 shows the starting substrate of the quantum dot wafers.
quantum dots are embedded near the center of the GaAs layer.
28
The InAs
Underneath the
GaAs layer is a sacrificial layer of Al 0. 9Gao. 1 As, which can be undercut using HF
to suspend the structures in the top 160nm GaAs layer.
Finally, all of this is on
top of a GaAs substrate. All the fabrication was done using the Technology Research
Laboratory cleanroom, which is part of MIT's Microsystems Technology Laboratories.
The fabrication process is the following:
1. Clean small 5 mm by 5 mm unpatterned chips with sonication in acetone,
methanol, and isopropyl alcohol, consecutively, for 5 minutes each.
2. Spin coat ZEP520A electron beam resist at 4000 rpm for 2 minute, then bake
at 180'C for 3 minute. This results in about 350 nm of ZEP520A film as resist
mask. ZEP520A is used since it has good resolution and high contrast, faster
write time than PMMA since it has a lower dose to clear, and better etch
resistance than PMMA.
3. Spin Espacer at 4000 rpm for 1 minute. This is to help with the conductivity
of the sample during the electron beam lithography write to prevent charging.
4. Use the Elionix ebeam writer to pattern the resist, using about 320
tC/cm 2
dose to clear.
5. Immerse in DI water for 1 minute to remove Espacer.
6. Develop in o-Xylene for 2 minute 30 seconds, followed by a 30 second rinse in
IPA to stop development.
7. Dry etch through the 160 nm GaAs layer using SAMCO ICP-RIE, using a
Cl2 /SiCl 4 /Ar dry etch chemistry.
8. Immerse the sample in 1% HF for 1 minute 30 seconds. This undercuts the
Al0 .9Ga 0 .1 As sacrificial layer in order to suspend the bullseye structures.
9. Remove the ZEP520A by immersing in 85'C NMP for 2 hours. Oxygen plasma
clean is avoided in order to not damage the quality of the top GaAs surface.
29
(a)
(b)
Figure 2-7: (a) Left: design, right: fabricated structures of "bullseye" circular grating
(b) Left: design, right: fabricated structures of "bullseye" circular grating with suspended
bridges that can be broken to systematically place the structure on a fiber facet.
Figure 2-7 shows the result of the fabrication (at least from a top-down view
using a SEM) of the QD circular grating structure. The fabricated structures look
very good, no residual resist or other debris.
2.4
2.4.1
Experimental Results
Optical Setup
For the experimental setup, an excitation laser at 852 nm is used. Collinear to the
path is a collimated white light source to illuminate the sample. The laser is reflected
off a two mirror galvos and into a 4F imaging system (the principle of the 4F imaging
is shown in Figure 2-8), followed by a 50x NIR microscope objective and onto the
sample. A galvos and 4F imaging system is used for confocal imaging since there is
no translational piezo stage for the sample in the cryostat. The galvos and 4F result
30
in an effective translation of the sample during imaging without actually moving the
sample. The 4F is two lenses placed at a sum of the focal distance of each of the
two lenses away from each other. Then, one lens is placed at a focal distance away
from the galvos, the other is placed at a focal distance away from the aperture of the
microscope objective. The galvos will give an angle to the laser entering the 4F. The
4F will do a correction such that the beam entering the objective will have that angle
without the translation with respect to the central axis.
Object space
Image space
Detector ens
Colector lens
P2
11
f2
1f2
Figure 2-8: 4F imaging configuration [10].
The emission and image of the quantum dots then goes through the objective, 4F,
and galvos. Afterwards, it goes into either a CCD camera, out-couples into a fiber
to a spectrometer, out-couples into a fiber to an APD counter, or into a free-space
spectrometer.
When the emission is out-coupled into a fiber to the spectrometer
or APD, the fiber acts as a spatial filter to get the same effect as confocal imaging
optics. On the other hand, when the emission is sent into a free-space spectrometer,
an actual confocal imaging system is used. Figure 2-9 is the experimental setup used
for characterizing the quantum dot chips. A portion of the microscope setup is on
top of an elevated optical platform so that the objective can be suspended over the
Montana closed-cycle cryostat, as shown in Figure 2-10.
All the beam paths are
aligned to travel parallel with the holes in the optical table. This is necessary for the
X and Y translational stages that we will discuss further: Part of the optics on top of
the elevated optical table are on top of a Y translational stage that travels parallel to
the beam path in order to roughly translate the optics along the Y axis with respect
to the sample in the cryostat. Part of the optics on top of the Y translational stage
31
are on top of a X translational stage that travels parallel to the beam path in order
to roughly translate the optics along the X axis with respect to the sample in the
cryostat.
Right before the free-space spectrometer, there is a lens that focuses the
collimated beam to a pinhole, followed by another lens to collimated the beam; this
is the confocal imaging optics.
To external
APD by fiber
Coupler
To external
spectrometer
by fiber
50/50
Beamsplitter
Coupler
~
Elevated
Montana closedcycle cryostat
Pinhole
7
Sml
Figure 2-9: Experimental setup for quantum dot experiments.
(a)
(b)
Figure 2-10: (a) Microscope objective directly over Montana cryostat. (b) Portion of setup
that transitions from the elevated optical platform to the optical table.
32
2.4.2
Spectroscopy Experiments
For the experiments to be described, the free space spectrometer was used for all
spectrum measurements, and the external APD was used for doing the confocal scanning. For the spectroscopy experiments, we first do a confocal scan zoomed out to
the largest field of view possible in order to see which bullseye has an enhanced fluorescence at its center. Since there should be a Purcell enhancement of about 20,
we would expect good structures to have a much brighter spot than the surrounding
unpatterned bulk QD regions. This is exactly what we see in Figure 2-ll(a) , where all
the bright spots coincide with the location of the bullseyes. After we know the general
proximity of each bullseye, we can zoom in to each individual bullseye by modifying
the scan area and increasing the resolution. This is done by finely controlling the
voltage applied to each galvos mirror, which finely tunes the galvos mirror positions.
Figure 2-ll(b) is a zoomed-in confocal scan of the fluorescence of a single bullseye
circular grating. We can see clearly that there is a significantly much brighter spot
at the center of the structure.
(a)
x10'
-1
(b}
x 10'
015
-0.6
016
-0.6
0.17
-0.4
0.18
~
~
-0.2
e2 0.19
~
0
:s;
""
0.2
0.2
0.21
0.4
0.22
0.6
0.23
0.6
0 24
-0.6
-0 6
-0.4
-0 2
0
0.2
0.4
0.6
0.8
0.42
1
0.43
0.44
0.45
0.46
0.47
0.46
0.49
0.5
0 51
Microns (um)
Microns (um)
Figure 2-11: (a) Confocal scan of the fluorescence of an array of bullseye circular gratings.
(b) Zoomed-in confocal scan of the fluorescence of one bullseye circular grating. Note: the
dimensions on the side are not the actual physical dimensions of the scan, but rather the
voltage applied to each galvos mirror.
Then, we can park the galvos mirrors such that the beam spot from the objective
(and the collection spot) is at the center of the bright fluorescence. I\ ext, we flip
33
the flip-mount mirrors such that the collection path goes into the confocal imaging
optics and into the spectrometer to take the spectrum. Figure 2-13 is an example of a
bullseye circular grating spectrum while Figure 2-12 shows the spectrum of the bulk
quantum dots for comparison. We see a significant resonance peak at around 935nm,
which is just 5nm off from the simulated spectrum shown in Figure 2-3(f). This is
reasonable considering slight fabrication imperfections. It looks like the peak width is
about 5nm, as simulated. However, this is not easy to see because the spectrum has
some of the bulk QD characteristics added to the resonance peak. This is probably
due to the excitation beam and collection spot size being bigger than the bullseye
structure. This can be fixed either by using a higher NA objective or reducing the
pinhole size in the confocal imaging optics.
Figure 2-12: Spectrum of the bulk quantum dots at an unpatterned area.
/
1500.
1 00
90
0050
0000
Figure 2-13: Spectrum at the center of a bullseye structure with a bright enhanced fluorescence spot.
34
Figure 2-14: Spectrum at the center of a bullseye structure with a bright enhanced fluorescence spot, using a higher density grating and lower pump power.
The next step for characterizing the bullseye structures would be to use a higher
density grating in the spectrometer in order to get a higher resolution spectrum.
Using this grating, the pump power is decreased until single exciton lines like the
ones shown in Figure 2-14 can be seen. At sufficiently low pump power, we should be
able to see a single exciton line that gets dramatically enhanced when the respective
QD overlaps with a cavity both spatially and spectrally. However, that is something
we have not been able to observe. Usually to get a QD that overlaps with the cavity
perfectly spatially, we would need to tune the QD emission wavelength by tuning the
temperature.
Nonetheless, this did not seem to work, and it did not appear as if
the QD emission spectrum was changing when the cryostat temperature was tuned.
A potential explanation for this is that perhaps the sample was not making a good
thermal contact with the cryostat cold head, so it was not actually at the temperature
we desired it to be. This is something to be sorted out in the near future.
Once we can determine from spectroscopy experiments that we have a QD that is
aligned perfectly spatially and spectrally to a bullseye, then the emission can be sent
to a Hanbury Brown-Twiss interferometer that uses APDs for detection to measure
the photon autocorrelation statistics to check the single-photon characteristics of that
QD. Once a good QD in a good bullseye structure is found, then we would pick-andplace the bullseye membrane onto a fiber facet and repeat the same experiments while
expecting higher collection efficiency. This can also be extended to Li et al.'s previous
work in which they demonstrated record-high photon collection rate from a single NV
35
center by using bullseye circular gratings [121. By integrating the bullseye structure
with an NV in it to the facet of a high NA fiber, we can expect to get an even higher
photon collection rate.
36
Chapter 3
Quantum Repeater using NV and
Wide-Bandgap Programmable
Nanophotonic Processor
3.1
Overview and Vision
For this portion of the thesis, I will highlight our efforts to create a quantum repeater
for long-distance quantum communication and distributed quantum computing. For
this, we will be using nitrogen vacancy centers in diamond as quantum memories.
We also need to be able to generate entanglement between two quantum memories
on-chip by entangling the photons that are entangled with each quantum memory. To
do so, we would need a wide-bandgap programmable nanophotonic processor (or circuit) that is capable of entangling visible wavelength photons between two quantum
memories on chip via a 50:50 splitter and detection via superconducting nanowire
single-photon detectors (SNSPDs) at the output arms.
As we have in our arsenal
the pick-and-place membrane transfer method, we can use different material systems
for this method by fabricating the different components separately and transferring
them to the host device with the programmable nanophotonic processor. As such,
we require the host device material to be a wide bandgap semiconductor, with high
37
thermal conductivity and small thermo-optic coefficient so that the entire system can
be placed in a cryostat and remain operational since the SNSPDs operate at cryogenic
temperatures. In addition, we require the host device material to have electro-optic
tuning capabilities in order to tune on-chip filters and phase shifters. Figure 3-1 is
an overview of the quantum repeater hardware that we propose. The AlN dynamic
photonic routing circuit is an optical mesh of cascaded tunable Mach-Zehnder interferometers with phase shifters for accurately tuning the output splitting. These phase
shifters are necessary since it is typically impossible to make directional couplers with
exact 50:50 splitting ratios, so the phase shifters help compensate for these fabrication imperfections. In addition, the programmable nanophotonic processors can be
programmed to implement any arbitrary unitary optical transformations.
Quantum Repeater Hardware
Nitrogen Vacancy in Diamond Qubits:
" NV-: ion 'trapped' diamond lattice
- Electron T2 -second
* Two-qubit gates & error correction
--
Electrical Control
Cavity Interface to Qu. Register
Optical Control
Couplers
QR1
repeater module
Detector
-
QR8
quantum registers
AIN Dynamic Photonic Routing
Control, Comm, Cooling
Figure 3-1: Overview of quantum repeater hardware, which uses nitrogen vacancy centers
in diamond as quantum registers, AIN photonic integrated circuit for dynamic photonic
routing, and SNSPDs as on-chip detectors.
38
3.2
Aluminum Nitride
For our host device material, we decided to use aluminum nitride since it has a large
bandgap of 6.2 eV, high thermal conductivity of KAIN= 285 W/m-K, small thermooptic coefficient of dnAIN/dT = 2.32 x 10-'/K, a fairly good electro-optic coefficient
of r 32 , r13 ~ 1 pm/V, and an added bonus of x(2) of about 4.7 pm/V. The large
bandgap means that AlN can operate in the ultraviolet, visible, and mid-infrared.
Its high thermal conductivity and small thermo-optic coefficients mean that we can
operate the entire device at cryogenic temperatures without the optical and physical
properties of the AlN changing too much. The electro-optic coefficient is useful for
tuning the optical properties of the AlN by applying an electric field across it. Finally,
even though its x(2) is no match for lithium niobate's X(2) of 16 pm/V, AlN is an
easier material to process and fabricate compared to lithium niobate. The X(2) allows
for frequency doubling, parametric frequency conversion, sum/difference frequency
generation, electro-optic modulators, optical parametric oscillators, frequency combs,
and much more. Frequency conversion is especially useful for interfacing the NV
quantum memories with telecom photons that are usually used as flying qubits for
long distance communication.
To scalably create many of these AlN programmable nanophotonic processor devices sometime in the future, we would need an AlN foundry process similar to the one
for silicon photonics of today, where there are multi-project runs that help distribute
fabrication costs amongst a larger number of end-users. One of the long term goals,
which I have started doing for this Master's Thesis, is to work with Sandia National
Laboratories to develop a large-scale AlN fabrication process.
3.2.1
Sandia National Laboratories' AIN Fabrication Process
Researchers at Sandia National Laboratories have already demonstrated the fabrication of AlN optomechanically tunable microdisks that can serve as optical filters.
Figure 3-2 is a depiction of this device from the side view with details of all the
materials that compose it. When a voltage is applied between the top electrode and
39
bottom electrode, piezoelectric effects would compress the disk slightly to tune the
resonance of the microdisk. In addition, the electric field across the AIN microdisk
in addition to the AlN's electro-optic properties would cause the refractive index of
the material to change, further changing the resonance of the microdisk.
Top electrode
N Bottom electrode
0 Aluminum nitride
M PECVD Silicon Nitride
4 PETEOS
M
Tungsten
N Silicon (substrate)
Figure 3-2: Complete device overview of Sandia National Laboratories' AlN optomechanically tunable microdisk that can serve as an optical filter.
Figure 3-3 shows the fabrication process for making these AlN optomechanically
tunable microdisks. For our nanophotonic processor, we need to consider these fabrication steps and have a design for each mask patterning step that would result in
the structures we desire.
1. Deposit nitride
4. Deposit, pattern, and
etch Ti/TiN/AICu/PE-SiNx
(bottom electrode+PECVDNitride)
2. Pattern and etch nitride
5
Deposit oxide
3. Deposit tungsten and
CMP back to planar
6. CMP oxide back to
planar
7. 1-1 Selectivity etch with
nitrogen drop endpoint
8. Deposit AIN
9. Pattern and etch down to
tungsten
10. Deposit AICu
11. Pattern and etch AICu
12. Etch down to nitride
13. Chemical dry etching using XeF2 gas
Figure 3-3: Fabrication process of Sandia National Laboratories' AIN optomechanically
tunable microdisk.
40
3.3
Mask Patterns for Sandia Process
In this section, we will go over the mask patterns for creating each Mach-Zehnder
interferometer (MZI) in the programmable nanophotonic processor. Figure 3-4 shows
the overall mask design for each Mach-Zehnder interferometer, along with labels for
each component.
Typically only the NV nanobeam cavity region, pump filtering,
and tunable microdisk resonators are connected to the first layer of MZIs. Also, the
SNSPD contact pads are typically only connected to the very last layer of MZIs. As
such, this is a condensed version of each MZI element in order to highlight all the key
components.
Microwave Stripline
Tunable Microdisk
Resonators
SNSPD
Contact Pads
hi
F"
NV Nanobeam Cavity
Directional
Coupler
*
Phase Shifter
Distributed Bragg Reflector
Figure 3-4: Condensed overview of the mask patterns for each MZI element. All masks for
the 6 layers are overlapped and displayed.
The NV nanobeam cavities are placed on top of tapered WG regions in the AlN
waveguide network in order to be integrated into the system by using the pick-andplace membrane transfer method highlighted in Figure 2-1. The result of this integration is depicted by Figures 3-5 and 3-6, the top-down view and side views, respectively.
The DC stark shift electrodes in close proximity to the NV nanobeam cavities are
used for tuning the NV in the nanobeam cavities. In addition, the DC stark shift
41
electrodes can also be used as microwave striplines for addressing the NV. In a similar
fashion, the SNSPDs are pick-and-placed on top of the SNSPD contact pads, and the
contact pads will be wire-bonded in order to electrically operate the SNSPDs. The
result of this integration is depicted by Figures 3-7 and 3-8, the top-down view and
side view, respectively.
The way the entire system would operate is the following:
1. Use the DC stark shift electrodes to tune the NV in the nanobeam cavities. In
addition, a microwave signal can be applied to address the NV in addition to
using a 532 nm green pump laser.
2. The photon emitted by the NV will propagate to the right and reach the Distributed Bragg Reflector. This is designed to filter out the green excitation laser
and allow the NV's 637 nm photon to pass through.
3. The photon will then come across two tunable microdisk resonators that serve as
tunable filters. The reason for this is that NVs suffer from a phenomenon called
spectral diffusion in which there are random jumps in the emission wavelength
of the zero phonon line.
As such, in order to get close to indistinguishable
photons between the two NVs, we need to use the filter to allow only photons of
the exact same wavelength to pass through. Two tunable microdisks are used
since they are expected to have a
Q
of only 10,000, so two tunable microdisks
might help with getting a large enough extinction ratio.
4. The photon reaches the first directional coupler of the MZI. The fabricated
directional couplers are not expected to have 50:50 splitting due to fabrication
imperfections.
5. The phase shifter then applies a phase shift to the photon either through heating
the waveguide region by applying a large current through the metal contact
pads or through applying an electric field across the waveguide region by metal
contact pads to take advantage of AlN's electro-optic coefficient.
6. The photons then reach the second directional coupler of the MZI.
42
7. Finally, the photons reach the SNSPDs at the very right to be detected.
Top-Down View Of Microwave Stri plines
Gold (or aluminum) microwave striplines
*
[-
*** Not to scale ***
Diamond nanobeam cavity
AIN
50 um
sapphire
Figure 3-5: Top-down view depicting a NV nanobeam cavity membrane integrated to the
AlN photonic waveguide network. This also shows the proximity of the microwave striplines
with respect to the NV nanobeam cavity.
All in all, entanglement is created between the two NV quantum memories by
entangling the two respective photons associated with each quantum memory. This
is done by essentially doing a Bell State measurement using the MZI and SNSPDs to
collapse the two photons into a Bell State. In this scheme, the MZI acts as a 50:50
beam splitter that can be tuned to have exactly a 50:50 splitting ratio by tuning the
phase shifters.
Next, let us look at the pattern for each layer in detail. Figure 3-9 shows the mask
patterns for the first 5 layers of the chip fabrication. Figure 3-9(a) is the first layer
pattern for etching the silicon nitride layer in step 2; this is also the pattern for the
tungsten that will be deposited into the etched silicon nitride region. Figure 3-9(b)
is the second layer pattern for etching the bottom electrode in step 4. Figure 3-9(c)
is the third layer pattern for etching through the AlN and bottom electrode layers
and stopping at the tungsten layer in step 9; this is so the bottom electrode can
43
Side View Of Microwave Striplines
Gold (or aluminum) microwave striplines
*
[-, Diamond nanobeam cavity
Not to scale ***
M AIN
* Sapphire
50 um
50um
Figure 3-6: Side view depicting a NV nanobeam cavity membrane integrated to the AIN
photonic waveguide network. This also shows the proximity of the microwave striplines with
respect to the NV nanobeam cavity.
*** Not to scale ***
Top-Down View Of SNSPD Contact Pads
Gold (or aluminum) pads
" AIN
* Sapphire
[ ] SNSPD
- SNSPD is 174um x 126um
- Contact pads are 155um x
100um, spaced 50um apart
Figure 3-7: Top-down view depicting a SNSPD membrane integrated to the AIN photonic
waveguide network. The SNSPD gold pads make contact with the gold pads on the chip so
that the larger contact pads can be wirebonded to electrically operate the SNSPD.
44
Not to scale
*
**
Side View Of SNSPD Contact Pads
Gold (or aluminum) pads
* AIN
* Sapphire
7, SNSPD
SNSPD gold
174 um
_b
contact
Figure 3-8: Side view depicting a SNSPD membrane integrated to the AIN photonic waveguide network. The SNSPD gold pads make contact with the gold pads on the chip so that
the larger contact pads can be wirebonded to electrically operate the SNSPD.
make contact with the top electrode in order for voltage to be applied to the bottom
electrode. Figure 3-9(d) is the fourth layer pattern for the AlCu etch in step 10 for
defining the top electrodes. Finally, Figure 3-9(e) is the fifth layer pattern for etching
through the AIN and silicon dioxide layer and stopping at the silicon nitride layer
in step 12; this is the pattern for defining the AlN structures.
Likewise, Figure 3-
10(a) shows the rest of the fifth layer pattern that defines the AlN structures. One
additional process is done after step 13 in Figure 3-3, and that is to pattern, deposit
gold, and lift-off the gold to make the microwave striplines, phase shifter electrical
contacts, and SNSPD contact pads. Figure 3-10(b) shows the sixth layer pattern for
making this.
We have just gone through an overview of the components of the wide-bandgap
programmable nanophotonic processor. Chapter 4 will go into details of each component, as well as the design and simulations. In addition, Chapter 4 will go through
the in-house fabrication procedures for making the passive components of the AlN
photonic circuit since it is important to have fast prototyping capabilities, rather than
relying solely on multi-project fabrication runs from Sandia for chip production.
45
(a)
(b)
(c)
(d)
(e)()
Figure 3-9: Mask patterns for making the tunable microdisk. (a) Pattern 1 for the nitride
etch in step 2. (b) Pattern 2 for the bottom electrode etch in step 4. (c) Pattern 3 for
etching through the AlN and bottom electrode to the tungsten layer in step 9. (d) Pattern
4 for the AlCu etch in step 10. (e) Pattern 5 for etching through the AIN and oxide to the
nitride layer in step 12. (f) Overview of the mask patterns for each tunable microdisk. All
masks for the 6 layers are overlapped and displayed.
46
(a)
Li
i
(b)
WA
a,
I
Figure 3-10: Mask patterns for making the rest of the MZI. (a) The rest of pattern 5 for
defining the AIN structures. (b) Pattern 6 for the metal liftoff step after step 12.
47
48
Chapter 4
Passive Components of Aluminum
Nitride Photonic Integrated Circuit
4.1
Adiabatic Waveguide Taper
The diamond nanobeam cavity membranes with an implanted nitrogen vacancy center in the center will be pick-and-placed onto the AlN photonic integrated circuit at
a waveguide taper region that adiabatically transitions between the diamond membrane's waveguide mode and the AlN waveguide's mode. This design is taken exactly
from a previous publication in my group by Mouradian et al. in 2014 [141, with a
pertinent figure shown in Figure 4-1.
The optimal device geometry was found by
calculating the coupling efficiency from the fundamental TE mode of the diamond
microwaveguide and the SiN waveguide while sweeping both the diamond microwaveguide and SiN waveguide taper lengths. Since SiN and AlN have very similar refractive
indices at 637 nm (2.01 versus 2.15, respectively), we can expect the same waveguide
taper in SiN to behave closely when applied to AlN.
The paper showed that a 2 Lm gap in the SiN waveguide, a SiN waveguide taper
length of 5 pLm, and a diamond microwaveguide taper length of 6 tm would result in
a coupling efficiency of 41.5% coupled to each side of the SiN waveguide separated by
the gap (or 83% total into the SiN waveguide).
49
diamond micro-waveguides
SiN waveguides
w 0.86
C
0
0.82
---. NV to diamond
0 0.78
.560
-
diamond to SiN
600 640 680 720 760
Wavelength (nm)
Z
Figure 4-1: Adiabatic waveguide taper for coupling light efficiently from diamond nanobeam
cavities to AIN waveguide. This design is taken exactly as-is from Mouradian et al.'s 2014
paper [141.
Bragg Grating Filter
4.2
(a)
Thickness = 200nm
(b)
I
(c)
280nm
400nm
72nm
Effective mode index = 1 .89868
i
(d)
Effective mode index =1 810855
Figure 4-2: (a) Overall design of Bragg Grating filter, which is used for filtering the 532
nm green excitation laser and allowing the 637 nm NV fluorescence to pass through. (b)
Dimensions of the Bragg Grating filter, where the period is 144 nm, the original waveguide
width is 400 nm, the corrugated waveguide width is 280 nm, and the thickness of the
waveguide is 200 nm. (c) Electric field profile of the larger width 400 nm cross section,
which has an effective mode index of 1.89868. (d) Electric field profile of the smaller width
280 nm corrugated cross section, which has an effective mode index of 1.810855.
As shown in Figure 4-2, this is the design and Lumerical MODE Solutions simu50
I
I
lation results of the waveguide Bragg Grating filter. Figure 4-2(a) shows the overall
design and what it looks like when the Bragg Grating filter is repeated for 25 periods.
Simply put, the design is a strip of waveguide with periodic sidewall corrugations,
which results in a periodic modulation of the effective refractive index of the optical
mode. At each corrugation boundary, part of the travelling light is reflected, where
the relative phase of the reflected light is a function of the grating period and the
light wavelength.
As such, a Bragg Grating can be thought of as a 1D photonic
crystal, so the filtering property is a result of the photonic bandgap that is formed in
this structure. The repeated corrugation in the wavelength causes multiple and distributed reflections, and the reflected light interferes constructively in a narrow band
around the Bragg wavelength. Outside this wavelength band, the multiple reflections
interfere destructively and result in the light being transmitted through the grating.
Figure 4-2(b) shows the exact dimensions of the Bragg Grating filter, where the period is 144 nm, the original waveguide width is 400 nm, the corrugated waveguide
width is 280 nm, and the thickness of the waveguide is 200 nm. The rough design
was done by finding the neff of the region with the larger waveguide width of 400 nm
and the ne.U for the smaller waveguide width of 280 nm, followed by using the Bragg
condition:
o
=
A
=
2neff A
2
(4.1)
neff
where A0 is the wavelength of the green excitation laser we want to reflect and filter,
which is 532nm. nfeff is the effective refractive index of the complete Bragg Grating
filter, which we take to be approximately equal to the average of the effective mode
index of the wider and thinner cross sections of the filter. Finally, A is the grating
period. The transmission and reflection spectra of a Bragg Grating can be calculated
analytically using Coupled Mode Theory, which says that the reflection coefficient for
a grating of length L is
141:
51
~-ir sinh(-yL)(42
r
7 cosh(yL) + iA# sinh(-yL)
where -y 2
=2
-
32. r is the coupling coefficient of the grating, or the amount of
reflection per unit length. A,3 is the propagation constant when offset from the Bragg
wavelength, where Az = 0 - /o
<
0. If we want to get the peak power reflectivity
at the Bragg wavelength where r = -i tanh(sL), then we use:
Rpeak =
tanh 2 (L)
(4.3)
The bandwidth of the Bragg Grating filter can then be calculated by using:
2
7n =
7
2+
(4.4)
where ng is the group index. When the Bragg Grating is many periods long, which
means that n
>> 7, then we get that the bandwidth of the Bragg Grating filter
becomes:
2
A7 =
7ng
(4.5)
Hence, from the equation of the Bragg Grating filter peak power reflectivity at
the Bragg wavelength and the equation for the bandwidth, we know that higher
corrugation width results in an increased coupling coefficient K, which results in a
higher reflectivity and broader bandwidth. This is what we considered in designing
the Bragg Grating filter for filtering out the excitation pump.
Figure 4-3(a) shows the Lumerical FDTD simulation results of the Bragg Grating
filter, which was set to find the bandstructure spectrum at the band edge of k, = r/a.
The two peaks give the location and span of the band gap. Although this simulation
was done for an infinitely long periodic Bragg Grating with infinite periods, it serves
as a good approximation for how the Bragg Grating would behave when we do have a
52
(a)
90-
-Re(ts)
oe+0105e+O 104e*010-
/
(N
-
3e-0 10
2e+010-
e+V105.1
6
tl341
t.54
15 4.1
lambda
-
-6
(b)
line 0
0
5000 periods
0
C
f-403
0.112
US4
0.110
0.1
[).0
wavelengthi (microns)
00;2
0.;4
0
(C) -10
-- 20-
-30
50-
8000 periods
4
-0
O.12
6A4
0.
0.118
0.
wavelength (microns)
0A2
UA.4
Figure 4-3: (a) Bandstructure spectrum at the band edge k, = 7r/a.
spectrum for 5000 periods. (c) Transmission spectrum for 8000 periods.
(b) Transmission
sufficiently large number of periods. We can see from the images that the two peaks
are at around 531.8 nm and 532.8 nm, which means that the band gap covers the
wavelength of 532 nm of the excitation laser that we want to filter out. Figure 43(b) shows the Lumerical MODE Solutions simulation result for calculating the full
transmission spectrum given that the Bragg Grating filter is 5000 periods long. We see
that there is a dip for wavelengths between 529.7 nm and 532.8 nm and an extinction
ratio of about 58 db. Figure 4-3(b) shows the Lumerical MODE Solutions simulation
53
result for calculating the full transmission spectrum given that the Bragg Grating
filter is 8000 periods long. We see that there is a dip for wavelengths between 529.7
nm and 532.8 nm and an extinction ratio of about 61 db. In addition, Figure 4-3(b),
(c) show that there should be 100% transmission for 637 nm, which is the fluorescence
wavelength of the Nitrogen Vacancy center.
4.3
Disk Resonator
Nitrogen Vancancy centers in diamond suffer from a phenomenon called spectral
diffusion in which there are random jumps in the emission wavelength of the zero
phonon line. Several GHz wide spectral diffusion is typically an issue for implanted
NVs near the surface when pumped off-resonantly, which leads the zero phonon line
to broaden. This causes the photons emitted from the NV to no longer be indistinguishable [251. In order to combat this and to entangle two indistinguishable photons
from two different NV quantum memories, we will utilize disk resonators that can be
tuned electrically using ALN's piezoelectric properties.
4.3.1
Dependence on Coupling Gap
Figures 4-4, 4-5, and 4-6, highlight the dependence of the coupling gap and getting
critical coupling between the microdisk and the bus waveguides. For these designs,
we have two things to consider: 1. the microdisk has to be at least 30
tm in radius
since they need to be sufficiently large enough for electrical contacts to control the
piezoelectric properties and 2. the microdisk is expected to have a
Q
of around 10,000
since this is what was measured to be experimentally achievable by Sandia National
Laboratories' AlN fabrication efforts previously.
We obtain a
Q
of around 10,000
in the simulation microdisks by introducing a value in the imaginary portion of the
material refractive index to mimic loss in the material. Since we are expecting the disk
to have
Q
of 10,000, it was challenging to find the right coupling mechanism to get
critical coupling. Obviously a single point coupling scheme would not be sufficient
to load a disk with such high loss, so a wrap-around scheme has to be used.
54
For
OQ
M
amt34j(mricruls)
(C)
(c)
I
04 0I3
0
4 V 3 30 4'
04-1 UO000 U0003C
03OIQ
4rr33da(eOicrur
0)
Figure 4-4: (a) Simulation setup for a disk resonator of 30 tm coupled to two bus waveguides
by a coupling length of 12.3890 ptm and coupling gap of 200 nm. The input port is at the
top left, the through port is at the top right, and the drop port is at the bottom left. (b)
Transmission spectrum of the through port. (c) Transmission spectrum of the drop port.
these designs, we have two bus waveguides coupling to the microdisk, that way we
can either use the through port or the drop port for filtering. From 4-4(b), 4-5(b),
and 4-6(b), we see that we get closer and closer to critical coupling as we decrease
the coupling gap. However, we never actually get to critical coupling since we do
not get dips in the through port transmission spectrum that reach sufficiently close
to 0. Though we do for a coupling gap of 50 nm, the off-resonance transmission is
55
(b)
041
Iam(4da~micrcfl0)
(c)
U03
(
U.0
&0
004
04V24
2Ombra(rnicrons)
00303 VO402 ' . v j :
Figure 4-5: (a) Simulation setup for a disk resonator of 30 ptm coupled to two bus waveguides
by a coupling length of 12.3890 urm and coupling gap of 100 nm. The input port is at the
top left, the through port is at the top right, and the drop port is at the bottom left. (b)
Transmission spectrum of the through port. (c) Transmission spectrum of the drop port.
not 1 either, meaning we do not have critical coupling.
A coupling gap of 50 nm
is the minimum we are willing to consider since beyond that, the structures would
be difficult to fabricate, even with electron beam lithography. Ideally, we would use
a gap of 200 nm since that is the limit of optical lithography and something easily
achievable by electron beam lithography.
56
(c)5
r-lzI
'iI
ambda(microfl
)
0.4
Figure 4-6: (a) Simulation setup for a disk resonator of 30 pLm coupled to two bus waveguides
by a coupling length of 12.3890 pLm and coupling gap of 50 nm. The input port is at the
top left, the through port is at the top right, and the drop port is at the bottom left. (b)
Transmission spectrum of the through port. (c) Transmission spectrum of the drop port
4.3.2
Dependence on Coupling Length
Figures 4-7, 4-8, and 4-9, highlight the dependence of the coupling length and getting
critical coupling between the microdisk and the bus waveguides. The results from
Figures 4-7 is meant to be compared with those from Figure 4-6 since the coupling gap
is kept the same at 50 nm but the coupling length is changed to 60 ptm from 47.124 ptm.
In this comparison, we see that the on-resonance transmission dips remain sufficiently
57
(C)
Idrnda(ricronS)
Figure 4-7: (a) Simulation setup for a disk resonator of 30 Lm coupled to two bus waveguides
by a coupling length of 60 Rm and coupling gap of 50 nm. The input port is at the top
left, the through port is at the top right, and the drop port is at the bottom left. (b)
Transmission spectrum of the through port. (c) Transmission spectrum of the drop port.
close to 0 as the coupling length is increased. The difference is that the off-resonance
transmission becomes closer to 1 as the coupling length is increased, which means we
approach critical coupling. However, a coupling length of 60 pLm is near the limit for
a microdisk with radius 30 pLm without the two bus waveguides intersecting with each
other. As such, to get critical coupling to the microdisk, we also considered using only
one bus waveguide and using the through port for filtering, rather than having the
58
(b)000
8800]
lambda
0
'
(c)
!drntda(trk~runs)
Figure 4-8: (a) Simulation setup for a disk resonator of 30 im coupled to one bus waveguide
by a coupling length of 100 .m and coupling gap of 200 nm. The input port is at the bottom
left and the through port is at the bottom right. (b) Spectrum of the Q factor of the disk
as a function of wavelength. (c) Transmission spectrum of the through port.
option of using either the through port or drop port for filtering. Figures 4-8 and 4-9
show these results. Comparing these results with Figure 4-4 since these simulations
all have the same coupling gap of 200 nm but different coupling lengths, we see that
we do approach critical coupling as we increase the coupling length. Finally, we reach
critical coupling in Figure 4-9, where the coupling length is 150 urm. Figure 4-9(c)
shows that the off-resonance transmission is 1 while the on-resonance transmission is
59
(b)
(21)
lambo(micronfs)
Figure 4-9: (a) Simulation setup for a disk resonator of 30 gm coupled to one bus waveguide
by a coupling length of 150 pLm and coupling gap of 200 nm. The input port is at the bottom
left and the through port is at the bottom right. (b) Spectrum of the Q factor of the disk
as a function of wavelength. (c) Transmission spectrum of the through port.
very close to 0. In addition, Figure 4-9(b) shows that the Q of the microdisk indeed
is 10,000.
4.3.3
Plans for Better Design
Although we do get a design for critically coupling a waveguide to a microdisk with
radius of 30 ptm, this leaves no room for the drop bus waveguide.
60
After studying
this wrap-around coupling scheme a bit more, we realized that unlike a single point
coupling, it is necessary to match the phase of the waveguide and the phase of the
microdisk cavity. If somehow there is a phase mismatch of a multiple of r, the coupling
vanishes even if there is a strong field overlap [111. The phase matching condition is
dependent on the gap, waveguide width, and mode of the microdisk resonator. We
could also consider using a multi-mode interference (MMI) coupler to couple from the
waveguide to the microdisk. This is currently an on-going study for this project.
4.4
4.4.1
Directional Coupler for 50:50 Split
Analytical Calculations
A crucial component of a Mach Zehnder Interferometer is the directional coupler with
50:50 splitting ratios. Directional couplers are straight sections of two waveguides
where the evanescent modes of one waveguide overlap with the modes of the second
waveguide. As a result, light from one waveguide slowly transfers back and forth to
the second waveguide. The fraction of light from one waveguide that is transferred
to the other waveguide is a function of the distance between the two waveguides and
the length of the coupling region. For our directional coupler, we chose the coupling
gap to be 100 nm so that there is a sufficient amount of overlap of the evanescent
modes of one waveguide with the modes of the second waveguide.
To get a first
order estimate of the coupling length necessary to create a 50:50 splitting ratio, we
use Lumerical's MODE Solutions eigenmode solver to find the difference in index
between the two supermodes of the waveguide structure, which are known as the
symmetric and antisymmetric supermodes.
Figure 4-10 shows these results, where Figure 4-10(a) is the simulation setup,
Figure 4-10(b) is the real part of the Ey modal field of the symmetric supermode
with effective index of 1.816090, and Figure 4-10(c) is the real part of the Ey modal
field of the antisymmetric supermode with effective index of 1.810253.
From these
two values, we can use analytical formulas to calculate the necessary coupling length
61
(b)
1
06
-.
0
1
0
41
01
-
0
.0
0.5
0
1
1.
Effective Index: 1.816090
(c)
06
-02
02
y(microns)
Effective Index: 1.810253
Figure 4-10: (a) Simulation setup for solving the eigenmode of two straight waveguides
coupled evanescently to each other. (b) Real part of the Ey modal field of the symmetric
supermode. (c) Real part of the Ey modal field of the antisymmetric supermode.
to achieve 50:50 splitting ratios. Let us assume we have 100% of the power initially
62
in waveguide 1. Then, after the light from waveguide 1 passes through a directional
coupler of length L between waveguide 1 and waveguide 2, the power of light that is
now in waveguide 2 is given by:
P2 (L) = Po sin 2 (w7zon
(4.6)
where An is the index difference between the symmetric and antisymmetric supermodes, L is the length of the coupling region, Po is the input power, and AO is the
free space wavelength. Hence, if we manipulate Equation (4.6), we can calculate the
coupling length necessary to achieve any desired power coupling to waveguide 2:
L =
-
irAn
sin-
P_
(4.7)
Po
Therefore, if we want 50% of the light from waveguide 1 to couple into waveguide 2,
then we need the following length:
L =
L =
37msin~
0.637pm
1
-
(=~" 27.283ptm
7.53L
7r(1.816090 - 1.810253) sn
4.4.2
(4.8)
1/
Variational FDTD Simulations
In order to test the accuracy of our analytical results from (4.8), we did an optimization for finding the necessary 50:50 splitting ratios of the directional coupler using
Lumerical's 2.5D FDTD Propagation Method.
This variational FDTD solver effi-
ciently simulates the propagation of light in a guided structure. This is a good first
set of simulations since it is faster than the highly computationally intensive threedimensional FDTD method for solving large photonic structures, which is what we
have in this case since the coupling length is required to be 27.283
tm. For these
simulations, we assume that the waveguide bend that guides the two separate waveguides to the directional coupler section is 20 pm since AlN has a small index contrast
with air surrounding the structures, so we use a large bend radius to reduce propagation loss. When doing the optimization using the 2.5D variational FDTD solver, we
63
10
4
(m0
jJ
0-......................
.10
1
3
5
(d)
10(c)
1
181mbd3(mcr1
ns
1,1a Imbda(mlcrons)
0,.(e)
1)b~a(81
"11S
Figure 4-11: (a) 2.5D variational FDTD simulation setup for solving the splitting ratio of
a directional coupler with bend radius of 20 xm and coupling length of 60.673 m. Bottom
left hand is the location of the input mode of waveguide 1, bottom right hand is the location
of the output mode of waveguide 1, and the top right hand is the location of the output
mode of waveguide 2. (b) Electric field profile of the entire propagation structure. (c)
Transmission of power through the waveguide 1 input. (d) Transmission of power through
the waveguide 1 output. (e) Transmission of power through the waveguide 2 output.
found that 60.673 tm is actually the coupling length that results in a 50:50 splitting
ratio, as seen in Figure 4-11. We see in Figure 4-11(b) that the electric field profile
of the entire propagation structure has equal power splitting at the waveguide 1 and
waveguide 2 outputs. Figures 4-11(d) and (e) show the transmission of the power
through the waveguide 1 output and the waveguide 2 output, respectively, to confirm
that indeed there is a splitting of 50:50 of the power of light inserted at the waveguide
1 input shown in Figure 4-11(c).
64
102)
()(b
U
UO
02+1
U
2000
00-0
U50
- U0
0
-0
0 0 0 U0U
oamodacrns
a00 da(MtcrC~nco
i(e)
-500.............
t
-5103
0iO
U0
U
'O
UC;
.510
.01
.00.4
-501
-000
lx
Figure 4-12: (a) 3D FDTD simulation setup for solving the splitting ratio of a directional
coupler with bend radius of 20 pm and coupling length of 60.673 pLm. Bottom left hand
is the location of the input mode of waveguide 1, bottom right hand is the location of the
output mode of waveguide 1, and the top right hand is the location of the output mode of
waveguide 2. (b) Electric field profile of the entire propagation structure. (c) Transmission
of power through the waveguide 1 input. (d) Transmission of power through the waveguide
1 output. (e) Transmission of power through the waveguide 2 output. (f) Electric field mode
profile of the waveguide 1 input.
4.4.3
3D FDTD Simulations
Since there is a large discrepancy between the analytical calculations and the Lumerical 2.5D variational FDTD results, we also analyzed the structure in Figure 4-11(a)
using the Lumerical's 3D FDTD. This is the most accurate simulation that can be
run, though it is highly computationally intensive and takes a few days to run. Figure 4-12 shows the result of the 3D FDTD simulation that was performed on the exact
same structure as the one shown in Figure 4-12(a). We see in Figure 4-12(b) that
the electric field profile of the entire propagation structure does not have equal power
splitting at the waveguide 1 and waveguide 2 outputs. Figures 4-12(d) and (e) show
the transmission of the power through the waveguide 1 output and the waveguide 2
65
output, respectively, to confirm that indeed the splitting is not 50:50, rather it is 85:9.
Figures 4-12(f) is the electric field mode profile of the waveguide 1 input to show that
we are exciting the waveguide's fundamental single mode.
[016
02:
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Figure 4-13: (a) 3D FDTD simulation setup for solving the splitting ratio of a directional
coupler with bend radius of 20 tm and coupling length of 23.43 tim. Bottom left hand is
the location of the input mode of waveguide 1, bottom right hand is the location of the
output mode of waveguide 1, and the top right hand is the location of the output mode of
waveguide 2. (b) Electric field profile of the entire propagation structure. (c) Transmission
of power through the waveguide 1 input. (d) Transmission of power through the waveguide
1 output. (e) Transmission of power through the waveguide 2 output. (f) Electric field mode
profile of the waveguide 1 input.
Figure 4-13 shows the optimization for finding the necessary 50:50 splitting ratios
using Lumerical's 3D FDTD. We found that 23.43 tm is actually the coupling length
that results in a 50:50 splitting ratio. We see in Figure 4-13(b) that the electric field
profile of the entire propagation structure has equal power splitting at the waveguide 1
and waveguide 2 outputs. Figures 4-13(d) and (e) show the transmission of the power
through the waveguide 1 output and the waveguide 2 output, respectively, to confirm
that indeed there is a splitting of 50:50 of the power of light inserted at the waveguide
66
1 input shown in Figure 4-13(c). Figures 4-13(f) is the electric field mode profile of the
waveguide 1 input to show that we are exciting the waveguide's fundamental mode.
The result of this simulation is in agreement with our analytical calculations. In our
analytical calculations, we assumed that the waveguide 1 is coupled to waveguide 2
abruptly by the directional coupler. However, in the 3D FDTD simulations, we feed
the directional coupler with waveguide bends since introducing a second waveguide
abruptly usually results in scattering. As such, in the waveguide bend section, there
is already some evanescent coupling between the two waveguides, which makes the
necessary coupling length slightly shorter than the analytical results.
67
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Chapter 5
In-House Fabrication and Fast
Prototyping
In the nascent stages of a long-term project such as this, it is necessary to have
the capability of fabricating simple passive structures in-house in order to optimize
designs.
Otherwise, multi-project runs typically take 6 months to produce a chip,
which is not ideal when testing simple photonic structures in the beginning.
In
this section, I will go over the repeatable and high-quality fabrication procedure I
developed using MIT's Microsystems Technology Laboratories for making devices
that we can test. This capability will allow us to quickly make chips in less than a
day, test, and repeat for better and better optimizations. For our fast prototyping,
we will be using 200 nm of AlN on top of sapphire wafers, which we purchased from
Kyma Technologies.
The side view of the aluminum nitride on sapphire wafers is
shown in Figure 5-1.
AIN (200 [nm])
Sapphire
Figure 5-1: Starting substrate of the aluminum nitride on sapphire wafers.
69
5.1
First Generation Test Structures
For our first generation test structures, we want to check the AIN waveguide propagation loss, as well as the splitting ratio of the directional coupler. This is important to
test to see how good the fabrication process is, in addition to serving as the basis for
testing other photonic structures in the future, like Distributed Bragg Reflector filters
and microdisk resonator filters. Figure 5-2 shows the structure for testing waveguide
loss where we have a short waveguide section and two grating couplers on each side
for coupling light into and out of the waveguide. Figure 5-3 shows the structure for
testing the directional coupler splitting.
Figure 5-2: Structure for testing waveguide loss.
Figure 5-3: Structure for testing directional coupler splitting.
70
5.1.1
Grating Couplers
An important component for the first generation test structures is the grating couplers. Although for the final product of the programmable nanophotonic processor
we will do routing and detection of the NV emission all on-chip to minimize propagation loss, we need to use either grating couplers or edge couplers to couple light
into the AlN waveguide circuit during the prototyping stages to test each component.
Although edge couplers (or end-fire couplers) would be better since they have been
shown to have greater than 90% coupling efficiency, grating couplers are much easier
to make and can be placed anywhere on the chip, which is better for first generation
devices. However, we are in the process of incorporating edge couplers for future test
structures.
Grating couplers operate by taking advantage of the Bragg condition to scatter
light out of plane at each unit cell of the periodic grating. Using the Bragg condition
analytical equation, we can find the grating period for coupling light into and out of
the chip:
mA
sin(O) =
eff a
ccladding
(5.1)
where 6 is the angle of the emission from the grating coupler when coupling light from
a waveguide out of plane, neff is the effective waveguide index of the grating, ncladding
is the index above the waveguide, A is the wavelength of light we are interested in,
a is the pitch of the grating, and m can take on any value. Typically m = 1 to not
send out light at many different angles, but rather at only one particular angle (only
one order of light). We can manipulate the Bragg condition analytical equation to
get the grating pitch we need:
a =
A(5.2)
neff - sin(9)nciadding
We will arbitrary choose 0 to be 13.45 degrees and ncladding to equal 1 since we will
not cap the AlN waveguide with anything.
71
neff can be calculated by finding the
effective indices of the etched and unetched portion of each unit cell of the grating
coupler by using the Lumerical eigenmode solver in MODE solutions. Then, neff is
approximately the average of the two effective indices.
We designed these grating
couplers for both 532 nm light and 637 nm light.
In the case of 532 nm light, the effective index of the unetched portion is 2.005
and the etched portion is simply the air cladding since we will be using gratings in
which the etched portion is etched all the way to the bottom substrate. Hence, the
pitch should be the following in order to operate the way we want it to:
a=
0.532pm
(2.005 + 1)/2 - sin(13.45)(1)
-0.419pm
(5.3)
In the case of 637 nm light, the effective index of the unetched portion is 1.96 and
the etched portion is simply the air cladding since we will be using gratings in which
the etched portion is etched all the way to the bottom substrate. Hence, the pitch
should be the following in order to operate the way we want it to:
a -
0.637pm
(1.96 + 1)/2 - sin(13.45)(1)
=0.511pm
(5.4)
These grating designs were simulated using Lumerical's 2D FDTD by testing the
coupling from a waveguide source to out of the plane and by testing the coupling of
a beam from a Gaussian source into the waveguide mode. We found that for both
gratings, these values are around 25% to 35%. For the final grating coupler design,
we made the grating circular and tapered it from a 30 pim wide section to the 1 pm
wide waveguide.
5.2
Fabrication
Developing a reliable and repeatable in-house fabrication procedure was by far the
most difficult and time-consuming portion of this project. I experimented extensively
in trying to find the best electron beam resist and dry etch recipe to use.
To start off, I used ZEP520A as my resist, but I found that I would need over
72
800 nm thick ZEP520A to withstand the dry etch. I also tried using CF 4 /Ar etch
chemistry, as well as C12 /BCl 3 /Ar etch chemistry.
I found that C12 /BCl 3 /Ar etch
chemistry is not good for ZEP520A since it creates a build-up of material at etch edges
that cannot be removed, even with piranha. CF 4 /Ar does not have this problem, but
the ZEP520A etch resistivity is worst in CF 4 /Ar than in C12 /BCl 3 /Ar, so it actually
requires more than 1000 nm thick ZEP520A to withstand the dry etch. It is not ideal
to use such a thick resist since the resolution would be much worse.
Then, I moved on to using HSQ for the electron beam resist mask since HSQ
becomes similar to SiO 2 after development, which is much hardier against dry etching.
I found that HSQ has a better etch resistivity in C12 /BCl 3/Ar etch than in CF 4 /Ar.
Specifically, only 130 nm of HSQ is required for etching 200 nm of AlN, while 450 nm
of HSQ is not even enough to etch 140 nm of AlN. This is expected since CF 4 /Ar is
typically used for etching SiO 2 . Since the bottom substrate is sapphire for the AlN
wafers, I developed a novel fabrication process for removing the HSQ after fabrication
while keeping the underlying sapphire layer unharmed, which is highlighted in the
following:
1. Clean small 5 mm by 5 mm unpatterned chips with sonication in acetone,
methanol, and isopropyl alcohol, consecutively, for 5 minutes each.
2. Use the ebeam evaporator to evaporate 25 nm of Cr on top of the AlN layer at
a rate of 1 A/s.
3. Oxygen plasma etch the Cr layer for 1 minute and 100 W power.
4. Spin coat HSQ FOX-16 electron beam resist at 5000 rpm for 1 minute, then
bake at 80'C for 4 minute. This results in about 425 nm of HSQ film as resist
mask. HSQ is used since it has good resolution and high contrast and it has a
better etch resistance than ZEP520A and PMMA.
5. Use the Elionix ebeam writer to pattern the resist, using about 9600 kC/cm 2
dose to clear.
73
6. Develop in salty developer (1 wt% NaOH and 4 wt% NaCl) for 4 minutes,
followed by 10 minute rinse in DI water to stop development. Then, immerse
in methanol for 1 minutes, followed by air drying to not damage the structures.
The salty developer was formulated by Yang et al. in 2007 [271, and it was
shown to help greatly improve the resolution of HSQ masks.
7. Dry etch through the 25 nm Cr layer using Plasmaquest ECR-RIE, using a
C12 /0 2 dry etch chemistry. After this step, the side view of the chip looks like
the following:
HSQ
HSQ
Cr
Cr
AIN (200 [nm])
Sapphire
Figure 5-4: Side view of chip after HSQ patterning and Cr dry etch.
8. Dry etch through the 200 nm AlN layer using SAMCO ICP-RIE, using a
C12 /BCl 3 /Ar dry etch chemistry.
9. Remove HSQ layer by immersing the chip face down in a funnel in a Cr-7
(chrome etchant) bath for 1 hour. Then, flip the chip right side up in the Cr-7
bath and place the bath in a sonicator for 10 minutes.
10. Rinse the chip in DI water for 5 minute to wash away the Cr-7. Then, immerse
in methanol for 1 minute, followed by air drying to not damage the structures.
It is also possible to remove the HSQ with HF without etching the sapphire, so the
steps involving Cr as a liftoff layer can be skipped as well.
Figures 5-5, 5-6, and 5-7 show the microscope images of the finished product of
the AlN chip fabrication.
Figure 5-8 shows an atomic force microscope scan of a
portion of the AlN waveguide to demonstrate that the AlN layer is etched all the way
74
through and the structures are quite pristine with fairly straight sidewalls. Figures 59 shows an atomic force microscope scan of an AIN grating coupler. It might seem
that the gratings are not etched all the way through and that the sidewalls are not
very straight, but that is an artifact of the AFM scan. The AFM scans show that
the etch depth is about 220 nm to 230 nm, which is within the thickness uniformity
of 200 nm +/- 10% the wafers are rated at.
Figure 5-5: 50x microscope image of structure for testing directional coupler splitting.
Figure 5-6: 50x microscope image of structure for testing waveguide loss.
75
Figure 5-7: 100x microscope image of structure for testing waveguide loss.
50.0 m
200
1
150
1
10c
0
51
0
15
2
2.5
3
3,5
Grid Markers
- Marker 1
2
eylMarker
-Marker 3
Leel
4
45
pi
B
SResults
L vertDist
Height
e
ea
Vwlu
Name
1:
4,35 pm
Marker 4
Remtore
1,0.0
1.58 pm
2.37 pm
3,51 pmn
-222 nm
Yes
No
5.0 pm
Figure 5-8: Atomic force microscopy scan of a portion of the ALN waveguide.
50.0 nm
DataZoem
150
100
T'QT
0.5
1
1.5
2
B Grid Markers
Maker1
Marker 2
Marker 3
Marker 4
Reste
2.5
3
3.5
pm
0.217 pm
0.884 pm
2,25 pm
2.36pm
8Results
1E LvertDist 229 nm Yes No
10. 0
1: Height
-
J-.
.04.0 Jim
m Nav
__
VTe
I
Figure 5-9: Atomic force microscopy scan of an AIN grating coupler.
5.3
5.3.1
Experimental Results
Confocal Setup
For testing the AIN chips, we use a confocal microscope setup similar to the one
shown in Section 2.5.1, except the setup uses optical elements that are made for
76
Figure 5-10: Picture of the sample stage portion of the experimental setup, where the left
stage is the sample stage and the right Thorlabs stage is the piezo stage for positioning the
fiber.
visible wavelengths and the sample is mounted on a translational stage rather than in
a cryostat. This means that the confocal microscope setup does not have translational
stages for moving the optics with respect to the sample. Also, we use a lensed fiber
to pump light into the input grating coupler, while using the confocal microscope to
collect the light from the output grating coupler. The fiber has its own translational
stage for adjusting its position with respect to the AlN chip. Figures 5-10 shows the
Thorlabs piezo stage for positioning the fiber with high precision on the right and the
sample stage on the left, right underneath the objective. The sample stage is really
only for moving the sample up and down, or in and out of focus. Both of these stages
sit on top of another large translational stage so that once the ideal positioning of the
fiber is obtained with respect to the sample stage, the sample can be moved around
without perturbing its position with respect to the fiber.
77
5.3.2
Confocal Microscopy Experiments
For the confocal microscopy experiments, we first move the large translational stage
so that the confocal microscope objective is right above the location of the input
grating coupler. From there, we can see the input grating coupler on our white light
illumination field of view, as well as the excitation spot from the fiber. We tune the
position of the fiber until the excitation spot is entirely in the grating section of the
input grating coupler. Then, we move the large translational stage so that we are
viewing the output grating coupler on our white light illumination field of view. To
confirm the confocal scan encompasses the grating coupler, we excite with a 532 nm
laser and collect the reflection using the confocal microscope. The result is shown in
Figure 5-11.
x
-10
-8 i
106
2.6
2.4
-2.2
-6
2
1.8
-2
0~
1.6
1.4 R
1.
4
0.8
8
10
-10
M0.6
-8
-6
-4
-2
0
2
Microns (um)
4
6
8
10
Figure 5-11: Region of the output grating coupler in the confocal scan window. Image is
taken by exciting and collecting the reflection using the confocal microscope.
Afterwards, we excite with a 532 nm laser using the fiber so that light is pumped
at the input grating coupler. This time, we collect the light from the output grating
by using the confocal microscope. The result is shown in Figure 5-12. We do not see
any significant bright scattering at the grating region, which leads us to believe there
78
is something wrong with the test structures or with our experimental setup.
-101
-8
-16
-6
-16
-414
1
2
ES
10 a
0
4
6
6
4
8
2
10
- 10
-8
-6
-4
-2
0
2
Microns (urn)
4
6
8
10
0
Figure 5-12: Confocal scan when pumping with the fiber at the input grating and collecting
the light from the output grating by using the confocal microscope.
One room for improvement is to look at the design of the grating couplers once
again. It would be good to simulate the input grating using the exact specifications
of the lensed fiber and to simulate the output grating using the exact specifications
of the objective. In addition, I should look at extending the simulation to 3D FDTD
simulations in order to optimize the tapering section as well. Furthermore, the grating
couplers being designed and fabricated now have grating etches that goes all the way
through the ALN and stops at the sapphire substrate. However, the best grating couplers designed in silicon photonics often use partial etches since that is much better at
scattering the incident light out of plane. The downside of this is that the fabrication
usually requires two lithography steps. The plan would be to use a fabrication trick
demonstrated by Sapienza et al. in their 2015 Nature Communications paper that
would allow two different etch depths from just a single lithography step
1201.
We can also improve our experimental setup by using a lower NA lensed fiber for
pumping light into the input grating coupler. The reason is that the grating couplers
79
were designed with m = 1 so that light is not send out at many different angles, but
rather at only one particular angle. This applies to the input as well. Hence, for the
coupling to be more efficient, it would be best to use a lower NA lensed fiber that is
coupling light at a smaller range of angles into the grating coupler. The same would
apply for the objective at the output grating, so we should look into using a lower
NA objective as well.
80
Chapter 6
Conclusions and Future Work
In this thesis, we demonstrated efforts toward building a fiber-integrated single photon
source based on InAs epitaxially grown quantum dots, as well as building a quantum
repeater using nitrogen vacancy centers as quantum memories and AlN nanophotonic
devices as a wide-bandgap programmable nanophotonic processor. All these efforts
are steps toward the direction of building efficient light-matter interfaces for modular
quantum systems.
For the fiber-integrated single photon source, we have shown promising designs for
the device architecture, as well as a dependable and repeatable fabrication process
for making the bullseye membranes.
In addition, we were able to get promising
spectroscopy experiments using a scanning confocal microscope that has optical access
into the cryostat where the QD experiments were performed. The enhanced emission
of QDs in the bullseye structure and the fact that the bullseye spectrum matched
up closely with simulations show that the device fabrication was indeed very good.
However, more work has to be done on the experimental setup in order to characterize
the devices further and to determine if we have a QD that is aligned perfectly spatially
and spectrally to a bullseye structure. Then, we will need to pick-and-place these
structures onto a fiber facet and test to see if we do get a significantly higher-rate
of single photon production in this plug-and-play single photon source. Our plan is
to also extend this work to NWs in an attempt to demonstrate record-high photon
collection rate from a single NV center by integrating the bullseye structure with an
81
NV in it to the facet of a high NA fiber.
For the quantum repeater using nitrogen vacancy centers as quantum memories
and AIN programmable nanophotonic processor, we highlighted a long-term effort
with Sandia National Laboratories, as well as short-term efforts to demonstrate the
efficient routing and detection of photons from NVs in AlN photonic circuits. We
showed that using the tools in our arsenal, we can design all the necessary components for the Mach-Zehnder Interferometer array.
In addition, we were successful
in developing a repeatable and high-quality fabrication process at MIT for making
AlN devices for fast prototyping and optimization. Our immediate future goal is to
come up with a good way for coupling light into and out of the AlN chip for testing our structure, whether it is to develop better grating couplers or proceed with
a collaboration to integrate edge couplers. We hope to get a baseline value for the
device testing, so that we have a starting point to improve upon over the next few
years. Our vision is to one day create these quantum repeaters for aiding in the experimental demonstrations of various quantum information processing and quantum
communication protocols.
82
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